If you think about them, the scale fingerings actually do make sense don't they? They even feel correct when you play them.
I have found they have helped me a great deal, and I can play, or can attempt to play those pieces with the scales and arpeggios in them and I hated practicing them at the time. Now, I am grateful for them. If only I could get a decent recording up of one of those pieces on here! Wish it didn't have to cost so much. *humph*

Anyway, I also had a question, I am not real familiar with these forum sites, so I was wondering what Sticky meant. If you can answer, that'd be great! thanks

Since my last post, I have discovered t(without having looked at your pdf) the tips you have your chart and find them very useful in teaching the scales. I think it makes them less scary and we're all better off if we teach them that way. Using this means you are able to play 2 scales together with a bunch of black notes. For instance, you can play c sharp/ d flat, and g flat/f sharp together. I may try and record it.

Hey, is it normal when I play the ascending scales on C major, that during the 3-1 turn, the 3rd finger accidentally "brushes" against the key (with the part where the nail seperates from the finger)? Or should I relearn my scales so that my playing is clean and precise?

Here's a brief essay I put together, regarding the simplest way of organising scale fingering. Basically, virtually every scale fits into one of only two groups (aside from 2 exceptions out of 24 keys). I find that understanding those two groups saves a hell of a lot of time.

While I don't want to write off any value in the document posted earlier, I do find that the kind of approach featured there focuses on the differences unnecessarily. I think this makes it look a good deal more confusing than when you pinpoint the features that unify things to a far greater degree. When you require only two different mental organisations to cover everything (excepting B flat and E flat), it's far easier to grasp the patterns in a lasting way. The secret to realising how few coordinations are needed is not to worry about which fingers you start on, but notice how the thumbs are lined up- and derive all else from those.

Just my opinion, but I believe that scales should be learned/taught in the order of the Circle-of-5ths, starting with C major, then advancing sequentially through the incresing sharps to C# Major. Then start on F major and proceed to Cb major. Then go back and begin the relative minors. Why is this important? Because it lays the foundation for the closely related keys (the 2nd tetrachord of C major is the 1st tetrachord of G major; and the 1st tetrachord of C major is the 2nd tetrachord of F major, etc.), and it lays the foundation for the equality of keys. In otherwards, it's music-driven rather than mechanics-driven. Schemas of fingering organizations are always interesting, but from-begining-to-end a pianist has to know E major (for example) not for how it is like this scale or the next, but strictly because the E Major scale is intimately known by the pianist, seperate and apart. And the same goes for every other scale. BTW, there are only 61 scales (without mechanical permutations) that may be known (not counting exotic or invented scales): 15 major, 15 natural minor, 15 melodic minor, 15 harmonic minor and one fingering for all chromatic scales.

_________________Eddy M. del Rio, MD"A smattering will not do. They must know all the keys, major and minor, and they must literally 'know them backwards.'" - Josef Lhevinne

Just my opinion, but I believe that scales should be learned/taught in the order of the Circle-of-5ths, starting with C major, then advancing sequentially through the incresing sharps to C# Major. Then start on F major and proceed to Cb major. Then go back and begin the relative minors. Why is this important? Because it lays the foundation for the closely related keys (the 2nd tetrachord of C major is the 1st tetrachord of G major; and the 1st tetrachord of C major is the 2nd tetrachord of F major, etc.), and it lays the foundation for the equality of keys. In otherwards, it's music-driven rather than mechanics-driven. Schemas of fingering organizations are always interesting, but from-begining-to-end a pianist has to know E major (for example) not for how it is like this scale or the next, but strictly because the E Major scale is intimately known by the pianist, seperate and apart. And the same goes for every other scale. BTW, there are only 61 scales (without mechanical permutations) that may be known (not counting exotic or invented scales): 15 major, 15 natural minor, 15 melodic minor, 15 harmonic minor and one fingering for all chromatic scales.

Well, there are many valid ways to organise them. I'd personally suggest that majors should typically be practised with their relative minor, rather than separately. I'd also dispute that reference to tetra-chords is in any way "musically" driven. That's purely about a coincidence in the interval pattern that is mathematical by nature- as is evidenced by the fact that the whole thing falls apart when you proceed to minor scales. Music is not dependent on such things existing. The coincidental nature of tetrachords matters very little- especially considering that the same notes are frequently played within different fingers, upon recurrence in adjacent keys. Why not just relate it to the far simpler fact that a new sharp or flat is being added/subtracted on each occasion? The nature of tetrachords is certainly of intellectual interest, but I don't see that anything either immediately musical or practical hinges upon a necessity of noticing them.

I don't particularly follow your point about the danger of relating scales to others- seeing as you explicitly spent the entire first half of your post advising that scales be related to each other! This is why many would argue that it's a mistake to always proceed through in a single specific key order- precisely because of how much this associates scales with others. It's very important to practise them in totally random orders too- not just in a formal sequence.

My analysis of the scales has nothing to do with setting up a situation where scales can only be understood with reference to others. It simply provides the easiest way to understand each scale individually, with reference to the fewest necessary pieces of information about fingering- ie. with reference to thumb meetings. If you view fingering this way, all it takes a single note as a reference point for the first group, and two thumb notes for the second group. It condenses everything to absolute minimum possible- without leaving a pianist having to memorise all kinds of seemingly different fingerings (that are not different at all, if you simply change your focus to a different point within the scale). When understood this way, the fingering for any key can be mentally mapped out in full, in the very first instant of thinking about it. It makes it a lot easier both to organise the process of learning the movements and to maintain the memory of the movements (thanks to a handful of mental signposts).

I agree with much of what you have said actually. I too had my scales organized to practice based upon physical shapes and fingerings. However in the first sentence of my post I specified "learned/taught." To learn/teach D major, then Ab major, then B major, e.g. makes no sense to me. The issue of the tetrachords is theoretical, but demonstrates the nature of related keys; in fact one might say that related-keys are those that share a tetrachord. (I've never heard of applying tetrachords to minor scales.) The fact that a new sharp or flat is being added is precisely because of the structure of the tetrachords of the major scale (each WS, WS, HS, connected to eachother by a WS) must be maintained as we advance by 5ths. E.g., when we use the 2nd tetrachord of C major (G,A,B,C) as the first of a new scale, it is obviously now the start of G major. When we attempt to complete the scale with (D,E,F,G) we are confronted with the wrong sequence of intervals (WS,HS,WS). With a moment's thought, we can see that the proper intervalic sequence is fixed by raising the penultimate note by a half step: (D,E,F#,G) = WS,WS,HS. This is precisely why F# is the first sharp in the key signature. I think this is very important musically, as it is sequentially and systematically extended. (Many musicians don't know why F# is the first sharp and why Bb is the first flat.) As far as relating or not relating scales to one another, my point was that IMO, it is better to relate them musically initially when learning them rather than mechanically by fingering. I suppose you would teach B Maj/Min LEFT hand, and F Maj/Min RIGHT hand one after the other for mecahnical purposes. I would prefer to teach them in the sequence that relates them to their closely related keys.

As far as the thumbs issue, I again recognize this very important feature that you are discussing, so much so that I believe there is extreme value in practicing scales simply alternating the thumb and the other fingers. This is especially helpful for training the thumb to immediately pass under the hand to its next assignment as soon as it releases the note it played. (This can and should be done with arpeggios too.)

_________________Eddy M. del Rio, MD"A smattering will not do. They must know all the keys, major and minor, and they must literally 'know them backwards.'" - Josef Lhevinne

When I first learned scales back in the day, I began with B major. I was told that Chopin had taught this scale first since it was the one that lay the best under the hand. C major would be a difficult one to begin with IMO since it has no black keys to make thumb transmission easier. A scale I still hate is B-flat Major -- that one never feels right

I agree with much of what you have said actually. I too had my scales organized to practice based upon physical shapes and fingerings. However in the first sentence of my post I specified "learned/taught." To learn/teach D major, then Ab major, then B major, e.g. makes no sense to me.

Ah, fair enough. I wouldn't personally go right up to 7 sharps before introducing flat scales, but I'd certainly work on similar system of adding one at a time. Actually, I should also stress that my own lists were by no means meant to reflect any specific order. It's just to identify which of the two basic thumb principles each individual key follows.

Quote:

The issue of the tetrachords is theoretical, but demonstrates the nature of related keys; in fact one might say that related-keys are those that share a tetrachord. (I've never heard of applying tetrachords to minor scales.) The fact that a new sharp or flat is being added is precisely because of the structure of the tetrachords of the major scale (each WS, WS, HS, connected to eachother by a WS) must be maintained as we advance by 5ths. E.g., when we use the 2nd tetrachord of C major (G,A,B,C) as the first of a new scale, it is obviously now the start of G major. When we attempt to complete the scale with (D,E,F,G) we are confronted with the wrong sequence of intervals (WS,HS,WS).

I can see that this does work- but it really isn't "because" of the tetrachord. Otherwise, why would natural minors not abide by the same progressive system? The fact that natural minors operate the same way (regarding key signature) without involvement of tetrachords strikes me as a pretty conclusive proof that tetrachords are a mere consequence of the real cause of scales. The reason scales work as they do, with regard to black notes, is basically mathematics. Because of a symmetry issue, major scales work with tetrachords. However, natural minor scales work the same without them. The tetrachords are an incidental effect, not a cause- which is why natural minors (without the same symmetry) do not require such things, in order to include the very same order of accidentals. The tetrachord is just one part of the fact that every time you add/subtract a sharp or flat, only one single note is changed compared to the previous key. Why only focus on merely 4 similar notes when 7 out of 8 pitches are actually the same? I think it's actually rather simpler to notice that one note is changed each time, than to worry about a specific tetrachord. Personally, I judge all minors from the key signature and then think of any raised notes as adjustments. This way, you focus on the unity and further reinforce the principles from majors- rather than on the erratic way that minor scales might appear when viewed in an isolated context. It's far less confusing when your point of departure is the same basic key signature progression as for majors.

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With a moment's thought, we can see that the proper intervalic sequence is fixed by raising the penultimate note by a half step: (D,E,F#,G) = WS,WS,HS. This is precisely why F# is the first sharp in the key signature. I think this is very important musically, as it is sequentially and systematically extended.

Absolutely agreed. I just don't understand why this necessarily requires analysis of tetrachords. I think a change of one accidental makes it easier. Not that I'm disgusted by the concept of tetrachords or anything, but I don't think they are the foundation block so much an interesting pattern that can optionally be focussed upon. Personally, I'm more interested in the single note that is different to an adjacent key- not four specific notes of the 7 that are common to each. I don't see why these four notes are any more or less significant than the other three shared notes.

Quote:

As far as the thumbs issue, I again recognize this very important feature that you are discussing, so much so that I believe there is extreme value in practicing scales simply alternating the thumb and the other fingers. This is especially helpful for training the thumb to immediately pass under the hand to its next assignment as soon as it releases the note it played. (This can and should be done with arpeggios too.)

In major scales the simplest description of key progression is to say that every time you go up a fifth you have to either add one more sharp or subtract a flat (or if you go down a fourth you either subtract a sharp or add a flat). If tetrachords in any way "caused" that, this leaves absolutely no explanation as to why an identical rule holds together the progression between natural minors- despite an absence of tetrachords. We have similar cases (when viewed in terms of how key signatures progress), only one of which involves the notion of a tetrachord.

I think this is most concise proof I can think of, that the tetrachord is not a concept that causes anything- but rather an observation of an incidental detail. Quite why it does work out in a way where you end up keeping the same sharps and flats (plus or minus one) every time you move up a 5th or down a 4th, is probably one for an extremely advanced mathematician.

In major scales the simplest description of key progression is to say that every time you go up a fifth you have to either add one more sharp or subtract a flat (or if you go down a fourth you either subtract a sharp or add a flat).

You meant down a fifth, not a 4th. Interestingly this is one of the reasons that the subdominant is called such: it is the interval of the 5th below the tonic, hence sub-dominant.

It has been a refreshing discussion on things theoretical.

_________________Eddy M. del Rio, MD"A smattering will not do. They must know all the keys, major and minor, and they must literally 'know them backwards.'" - Josef Lhevinne

In major scales the simplest description of key progression is to say that every time you go up a fifth you have to either add one more sharp or subtract a flat (or if you go down a fourth you either subtract a sharp or add a flat).

You meant down a fifth, not a 4th. Interestingly this is one of the reasons that the subdominant is called such: it is the interval of the 5th below the tonic, hence sub-dominant.

It has been a refreshing discussion on things theoretical.

Oops- yep, up a fourth or down a fifth for the second of those statements.

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